Computer



F. W. BUBB Aug. 30, 1960 COMPUTER 2 Sheets-Sheet 1 Original Filed June9, 1950 VOLTAGE COMPARlNG AND AMPLIFYING MEANS INVENTOR.

FRANK W. BUBB Hula I- a yw? ATTORNEYS Aug. 30, 1960 B 2,950,862

COMPUTER Original Filed June 9, 1950 2 Sheets-Sheet 2 VOLTAGE COMPARING20 AND AMPLKFYING MEANS VOLTAGE (lOMFARlNg AND AMPLIFYING MEANS WWW/ginFIG. 3.

R a INVENTOR.

FRANK W. BUBB BY 67 1J3. FIG. 4. HWLMQ La,

ATTORNEYS COMPUTER Frank W. Bubb, Webster Groves, Mo., assignor toPhillips Petroleum Company, a corporation of Delaware Uriginalapplication June 9, 1950, Ser. No. 167,129,

now Patent No. 2,713,457, dated July 19, 1955. Di-

vided and this application Oct. 8, 1954, Ser. No. 461,068

(ilaims. (Cl. 235-180) This invention relates to computers. In onespecific aspect, it relates to vapor-liquid equilibrium computers. Inanother specific aspect, it relates to electrical circuits for carryingout the computing operations.

This application is a division of my copending application, Serial No.167,129, filed Tune 9, 1950, now Patent No. 2,713,457.

In many practical operations in refining, chemical, and otherindustries, it is of great importance to determine the composition andamount of liquid and vapor phases in a vapor-liquid equilibrium mixture.In general, the overall composition and total quantity of the mixtureare known, from which data the total number of mols in the mixture andthe total mol fraction of each component in the mixture may readily becalculated. Furthermore, the equilibrium constant for each component atthe particular temperature and pressure involved are either known or maybe calculated readily from known data. The computer of this invention,upon being supplied the equilibrium constant of each component at thetemperature and pressure involved, the total mol fraction of eachcomponent in the mixture, and the total number of mo ls in the mixture,calculates the mol fraction of each component in the liquid phase, themol fraction of each component in the vapor phase, and the total numberof mols of the mixture in the vapor phase or in the liquid phase. Oncethe mol fractions are known, the parts by weight or percentage of eachcomponent in the gas and liquid phases may easily be determined, if itis necessary to do so.

The computer circuits described herein, however, are not restricted tothe solution of the vapor-liquid equilibrium problem but may be utilizedto solve many equations of similar form. Moreover, certain improvedfeatures of my computer are applicable to computers solving diversifiedproblems not closely related to the solution of the vapor-liquidequilibrium problem.

It is an object of the invention to provide an improved computersuitable for solving the vapor-liquid equilibrium problem.

It is a further object to provide electrical computing circuitsapplicable both to the vapor-liquid equilibrium problem and to otherdiversified problems in the computer art.

It is a still further object to provide apparatus which is rapid andreliable in operation, of rugged construction, and which utilizes aminimum number of circuit components.

Various other objects, advantages and features of the invention willbecome apparent from the following detailed description taken inconjunction with the accompanying drawings, in which:

Figure 1 is a block diagram of the computer assembly;

Figure 2 is a schematic circuit diagram of one of the computing units ofFigure 1;

Figure 3 is a schematic circuit diagram of a modified computer unitsuitable for use in the apparatus of Figure 1; and

Patented Aug. 30, 1969 Figure 4 is a schematic diagram of a circuit forincreasing the spread of a potentiometer over a preselected part of itsrange.

In a vapor-liquid mixture containing several components, each componentdoes not behave independently of the other components as regards itsdistribution between the gas and liquid phases. In particular, thefollowing relationships hold for each component in the vaporliquidmixture:

KIZI

of the mol fractions in the vapor phase is 1. That is,

and

y1+y2+ +II11= where there are 11 components in the mixture.

In carrying out my invention, a plurality of computer units 19a, 10b, isprovided, one for each component in the mixture. The total mol fractionsZ Z 2,, of the respective components are set upon dials 11a, 11b, 1111,the mol fraction of the first component being set on dial 11a, the molfraction of the second component being set on dial 11b, and the molfractions of the remaining components being set on dials 11c to 1111,respectively. In similar fashion, the equilibrium constants K K Kn areset upon dials 12a, 12b, 1211, the constant for the first componentbeing set upon dial 12a, the constant for the second component being setupon the dial 12b, and the constants for the remaining components beingset upon dials 12c to 1211, respectively. The computer units 10 are alsoprovided with dials 13a, 13b, 1311 which are ganged and movable as aunit bya crank 13x, the setting of these dials being representative ofv, the total mol fraction of vapor in the mixture. Finally, the computerunits are provided with reversing switches 14a, 14b, 1411, the functionof which will be explained hereafter.

A constant voltage is supplied to each computer unit 10 by a battery orother voltage source 15, one terminal of the battery being grounded at16 and the other terminal being connected by a common conductor 17 tothe respective computer units, the battery circuit being completed foreach computer unit by a ground lead 18.

In a preferred embodiment of the invention, the computer units produceoutputs at terminals 19a, 19b, 1911 equal to the product of the batteryvoltage E and the mol fraction of the component under consideration inthe liquid phase. Thus, for example, the voltage at terminal 1911 may berepresented by E x and the voltage at terminal 1911 may be representedby E x Each such output voltage represents the relationship shown inEquation (1) between the variables determining the mol fraction of thecomponent in the liquid phase, this result being accomplished by thecircuits shown in Figures 2 and 3, which will be described hereinafterin detail. Moreover, the computer units produce voltages at output equalto the product of the battery voltage and the mol fractions of therespective components in the vapor phase. Thus, for example, the voltageat terminal Zita may be represented by E y and the voltage at terminalZtln may be represented by E y It will be understood that these voltagesare taken with reference to a ground connection, as indicated at 21.

A multi-gang switch 22 is provided to connect selectively the terminals1% and to the respective leads 23a, 23b, 2321, these leads beingconnected through resistances 24a, 24b, 2411, respectively, to a commonconductor 25. The individual resistances 24 are all of equal ohmicvalue, and this ohmic value is substantially higher than the resistancesof the circuits making up the computer units 10. When I speak of theseresistances as having a high ohmic value, I mean sufficiently high thatthe current flow therethrough is negligible, whereby this current doesnot disturb the voltages existing at various points within the computerunits, within prescribed limits of accuracy. The common conductor 25 isconnected through a galvanometer G to the contactor of a potentiometeras, one fixed terminal of which is grounded, and the other fixedterminal of which is connected to the ungrounded side of battery 15.

In the operation of the circuit of Figure l, potentiometer 26 isadjusted so that a voltage is applied to one terminal of galvanometer G.Thereupon, crank 13x is adjusted until a null reading is obtained on thegalvanometer. It will be understood that the described adjustment ofcrank 13:: changes the value of v in each of the computer units, thesettings representing K and Z remaining unchanged. When a zero readingof the galvanometer is obtained, conductor 25 is also at the potentialWhen the circuit is thus balanced, the voltage drop across resistor 24ais which equals i r, the product of the current i through resistor 24aand its resistance r.

Adding these relationships for each of the resistors 24a, 24b, 24a, itis evident that ne1+a+ +xa =ret+a+ +t.)

Since the circuit is balanced, the sum of the currents (i +i +i equalszero, with the result that (x +x +x )=1. That is, when the crank 132: isturned to the proper value of v, the circuit is balanced and the sum ofthe mol fractions of the various components in the liquid phase is equalto unity. Accordingly, the value of v satisfies Equation (3), and thepotentials E x correctly represent the mol fractions of the respectivecomponents in the liquid phase. Similarly, when switch 22 is moved intoengagement with the terminals 20 and crank 13x is adjusted until thecircuit is balanced, the same value of v is found to satisfy Equation(4) and the potentials E y correctly represent the mol fractions of thecomponents in the vapor phase.

Assuming that the circuit has been balanced with switch 22 in its upperposition, the value of v is read from any one of the dials 13. I alsoprovide a servomechanism unit for reading the values of x x x,,. Thisunit includes a switch 28 having an unconnected contact point 28a andhaving other contact points connected to leads 23a, 23b, 23m byconductors 29a, 29b, 2%, respectively. The arm of switch 28 is connectedto the input circuit of a voltage comparing and amplifying means 30,this input circuit also being connected by a lead 31 to the contactor ofa potentiometer 32, the fixed terminals of which are connected to abattery 33. Voltage comparing means 30 can be of the form shown inElectronic Control Handbook, Batcher and Moulic, p. 298, for example.Terminals A, A of Figure l3-V of this reference correspond to terminals28 and S l of Figure l. A motor 34, driven by the output of means 36),

is mechanically coupled to the arm of potentiometer 32 and causesmovement of this arm to a position where the voltage at conductor 31equals the voltage at the arm of switch 28. The motor is alsomechanically coupled to a dial 35 and, when the input voltage to means33 is zero, the motor is stopped, and the dial indicates a fractionequal to the voltage applied to the arm of switch 23 divided by thebattery voltage E Accordingly, as the switch arm is moved successivelyto its contact points, the values of the mol fractions x x x are readupon dial 35. Similarly, when switch 22. is in its lower position, thevalues of mol fractions y y y are read upon dial 35 as the arm of switch28 is moved successively to the different contact points.

In the overall operation of the computer, the values of K for therespective components of the mixture are set upon the dials 12 and thetotal mol fractions of the respective components are set upon the dials11. If it is desired to determine the mol fractions of the variouscomponents in the liquid phase, switch 22 is moved to its upper positionand the circuit is balanced. by adjustment of crank 13x untilgalvanometer G reads zero. Thereupon, the correct value of v is read onthe dials l3 and the values x of the mol fractions of the components inthe iquid phase are read by moving switch 28 to its several positionsand observing the readings on dial 35. Thereupon, if desired, switch 22may be moved to its lower position, and crank 13x adjusted until a nullreading is obtained upon the galvanorneter. The value of v upon thedials 13 should then agree with the value previously obtained withswitch 22 in its upper position. Thereupon, the values of the molfractions of the components in the vapor phase are read on dial 35' bymoving switch 23 successively to its different positions. Of course, thevalues of y y y may be obtained simply by multiplying the values of x xx by the equilib rium constants K K K respectively. Thus, the secondbalancing operation is useful primarily as a check upon the accuracywith which the coefficients were set into the computer.

In Figure 2, I have shown a circuit suitable for use as any of thecomputer units 10 when neither the equilibrium constant nor total molfraction of liquid or vapor has an abnormal value. In this figure, partssimilar to those described in Figure 1 are indicated by like referencecharacters. It will be noted that the voltage E of battery 15 is appliedto one fixed terminal of a potentiometer 37 which is controlled by adial 1-1, Figure 1, the other fixed terminal of the potentiometer beinggrounded at 18. The contactor of potentiometer 37 is connected by a lead39 to the input circuit of a voltage comparing and amplifying means 40which corresponds to means 38 of Figure 1. For purposes of explanation,the potentiometer settings are indicated on the figure as fractions, Zrepresenting the fraction of the total resistance of potentiometer 37between the contactor and ground, while (1 Z) represents the fraction ofthe total resistance connected between the contactor and the upper fixedterminal of the potentiometer. Thus, if Z equals one-third, thecontactor is positioned one-third of the way up from the grounded fixedterminal. The legends applied to other potentiometers in the circuitindicate fractions of the total potentiometer resistances in a mannersimilar to that already described.

It will be evident, therefore, that the voltage at conductor 39 is Ztimes the total voltage E impressed across potentiometer 37, that is, ZE

Conductor 17 also extends to one fixed terminal of a potentiometer 41,the other fixed terminal of which is grounded at 42. The contactor ofpotentiometer 41 is connected by a lead 43 to one terminal of areversing switch 14. Conductor 43 also extends to one fixed terminal ofa potentiometer 44 which is controlled by a dial 12, Figure 1, the otherfixed terminal of potentiometer 44 being grounded at 21. The contactorof potentiometer 44 is connected to a lead 46 which extends to a secondterminal of reversing switch 14- and to one fixed terminal of apotentiometer 47 which is controlled by a dial 13, Figure l, the otherfixed terminal of potentiometer 47 being connected to lead 43. Thesecond terminals of reversing switch 14 are connected to outputterminals 19 and 20. The contactor of potentiometer 47 is connected by alead 48 to the input circuit of means 40 and the output of means 40drives a servomotor 49 which is mechanically connected to the contactorof potentiometer 41.

The arrangement of the described servomechanism including means 41) andmotor 49 is such that the motor moves the contactor of potentiometer 41,thereby varying the voltage applied across the network consisting ofpotentiometers 44 and 47 until the voltage applied to conductor 48 isequal to the voltage applied to conductor 39. When the resultant voltagebecomes zero, the voltage at conductor 48 is equal to ZE movement of themotor is stopped, and the circuit is balanced.

In accordance with the invention, the resistance of potentiometer 47 issubstantially higher than the resistance of potentiometer 44. When Isay, in the appended claims, that the potentiometer 44 is of lowresistance and the potentiometer 47 is of high resistance, I mean thatthe resistance of potentiometer 47 is sufficiently high that the currentfiowing therethrough has a negligible efiect upon the voltage at thecontactor of potentiometer 44. This result may be accomplished, to anydesired degree of accuracy, by proper selection of the ohmic values ofpotentiometers 44 and 47. Accordingly, the voltage E equals BB Thevoltage ZE at the contactor of potentiometer 47 is, therefore, equal toThe mol fractions v and Z necessarily lie between zero and one. Hence,there is ordinarily no difliculty in setting these fractions upon theproper potentiometer. However, the equilibrium constant K may vary froma small fraction to a very large number. When K lies between zero andone, it is set as B upon the potentiometer 44 and the mol fraction v isrepresented by A. Thus, substituting A=v, B=K in Equations 5 and 6 Theseoutput voltages appear at the terminals 19 and 20, respectively, and arethe same as set forth in connection with Figure 1 so that the computerunit of Figure 2 functions in the manner already described as any of thecomputer units 10 in Figure 1, provided, however, that the value of Kfor any such unit is within the range of zero to one.

Where the value of K for a particular component is greater than one, thepotentiometer 44 is set to the value and the setting of potentiometer 47represents the value A i=lv. Substituting these values in Equations 5and 6 gives It will be noted that this circuit operates in precisely thesame manner as already described except that the po tential y E appearsas voltage E instead of voltage E while the potential x E appears asvoltage E instead of as voltage E When one or more components has avalue of K greater than one, reversing switch 14 is positioned in theone or more corresponding units It) so that the voltage E x appears atterminal 19 and the voltage E y appears at terminal 20, as described inconnection with Figure 1. This reversing switch should also incorporatea unit for reversing the connections to the fixed contacts ofpotentiometer 47, which unit is not shown on the drawing for purposes ofsimplicity. In this connection, it will be noted that all thepotentiometers 47 of the several computer units are ganged and operatedby crank 13x together with dials 13. However, A represents v when theequilibrium constant is less than one whereas A represents (lv) when theequilibrium constant is greater than one. When the connections to thefixed contacts of potentiometer 47 are reversed as in the case of anequilibrium constant greater than one, the V scale of the potentiometerof this unit is consistent with the V scale of the other potentiometers.

As previously explained, the dials 13, which control the potentiometers47 of the respective computer units, are moved in unison when thecircuit of Figure l is balanced. Such movement of potentiometer 47,Figure 2, produces a continuous and automatic rebalancing of the circuitof Figure 2 in accordance with the movement of crank 13x. The speed ofoperation of motor 49' is such that there is no discernible lag betweenthe movement of dials 13 and the subsequent rebalancing of the computerunit circuits.

When the circuit of Figure 2 is balanced, it will be noted that avoltage from potentiometer 41 is supplied to the network includingpotentiometers 4-4 and 47 across potentiometer 44. The function ofpotentiometer 47 is to pick ofi a preselected portion of the voltageexisting between the contactor of potentiometer 44 and lead 43 whosevoltage is derived from potentiometer 41, thevoltage thus picked upbeing compared with a reference voltage developed across potentiometer37 to produce a voltage difierence which, through the medium of means 40and motor 49, adjusts the voltage supplied to the potentiometer network44, 47 until the voltage difierence between leads 39 and 48 iseliminated. It will be evident to those skilled in the art that thisprinciple of operation is applicable to various types of computers,other than a vapor-liquid equilibrium computer.

The computer unit of Figure 2 is sufficient for the great majority ofcomponents found in the usual equilibrium mixture of vapor and liquid.However, there are some special cases where the computer unit of Figure2 is somewhat insensitive. For example, if the equilibrium constant of aparticular component approaches Zero and the total mol fraction of themixture in the vapor phase approaches one, the denominator of the vaporequilibrium equation approaches zero and the circuits are some whatinsensitive. This corresponds physically to a mixture where onecomponent is practically involatile and nearly all the remainder of themixture is in the vapor phase. In accordance with my invention, thecomputer unit for any such component is made more sensitive in theregion of interest in the manner illustrated by Figure 3.

In Figure 3, conductor 17 is connected to one fixed terminal of apotentiometer 52, the other fixed terminal of which is grounded at 18,the contactor of potentiometer 52 being connected by a lead 54 to means40, motor 49, and potentiometer 41 in the manner described in connectionwith Figure 2. A potentiometer 55 has one fixed terminal grounded andits other fixed terminal connected to conductor 43, the contactor ofpotentiometer 55 being connected by a lead 56 to one fixed terminal of apotentiometer 57, the other fixed terminal of which is connected to alead 58. The contactor of potentiometer 57 is connected by a lead 59 tothe input circuit of means 40. A potentiometer 6t? has one fixedterminal connected to conductor 43 and its other fixed terminalgrounded, the contactor of the potentiometer being connected through alead 61 and a fixed resistance 62 to lead 58. A fixed resistance 63 isconnected between conductors 43 and 58.

The potentiometer 52 is set to represent so that the voltage at lead 54is f Eo 2 Where 7 represents a scale factor for increasing thesensitivity of the potenticmeters. Means 40 and motor 49 operate, inconjunction with potentiometer 41, in the manner described in connectionwith Figure 2 to vary the voltage at conductor 43 until the voltage atconductor 59 is equal to the same as the voltage at lead 54. The ohmicvalues of potentiometer 57 and fixed resistors 62 and 63 are high ascompared with the ohmic values of potentiometers 55 and 60 with theresult that the small current fiow through the first mentioned resistorshas a negligible effect upon the voltages at conductors 56 and 61.Accordingly, the voltage at conductor 61 is MV where V is the voltage atconductor 43, while the voltage at conductor 56 is DV Preferably, fixedresistance 62 has one-half the ohmic value of potentiometer 57 whileresistance 63 has one-third the ohmic value of potentiometer 57.Furthermore, assuming that the voltage at conductor 58 is V the currentthrough potentiometer 57 plus the current through resistance 63 equalsthe current through resistance 62. Thus,

Furthermore, the voltage v at the contactor of potentiometer 57 may berepresented by the following equation: V =CV +(1C)DV 12) SolvingEquations 1'1 and 12 for V yields the following expression:

3 'In this circuit, potentiometer 57 is set so that C=f(l-v). As stated,v is approximately equal to one so that the small difference between vand one is multiplied by the factor 7", which may be 10, or 1,000,

7 thus making it possible to set this number upon potentiometer 57 withmuch greater ease and accuracy. Potentiometer 55 is set so that wherebyK which is, as stated, closely equal to zero, is multiplied by thefactor thus making it much easier to set potentiometer 55. Potentiometer60 is set so that M=(1.25f-1.5)K, and V of course, is equal to Thisvoltage is applied through a switch 43a to a terminal 19 of Figure 1,and the unit of Figure 3 is used for each component having a value of Kclose to zero Where the value of v is close to one. Thus, the circuitpermits the described values of v and K to be set with a much higherdegree of accuracy While still producing the same output at terminal 19as the unit of Figure 2. It will be noted that there is no point uponthe network of Figure 3 Where the potential is equal to y E Thus, whenone or more of the units of Figure 3 is utilized in the computer ofFigure 1, the values of y, the mol fraction in the vapor phase of thevarious components, cannot be read from the computer. However, thesevalues may be readily obtained merely by multiplying each value of x,for example x by its corresponding value of K, for example K It will befurther noted, in connection with Figure 3,

that the setting C of potentiometer 57 corresponding,

by proper choice of the direction of shaft rotation, to the setting A=vof potentiometer 47 of Figure 2 is fv. This would prevent proper jointadjustment of the potentiometers of the several computer units by thecrank 13x, since the potentiometer 57 would have to be rotated 1 timesas fast as potentiometer 47 of Figure 2 to produce a correspondingchange in the fraction represented thereby. This difliculty can beovercome by gearing the potentiometers 47 to the crank in such fashionthat the contactor movement is times as fast as contactor movement ofthe potentiometers S7 of the computer units of Figure 3. Alternatively,the same result may be accomplished electrically by substituting thecircuit of Figure 4 for the potentiometer 47 of Figure 2. This circuitincludes a potentiometer 65 of the same ohmic value as the potentiometer47 in Figure 2. Assuming that the resistance of this potentiometer is R,it is shunted by a fixed resistance 66 having an ohmic value of theseshunted resistances being connected in series with a fixed resistance 67having an ohmic value of (f-U f The total resistance of this combinationis R but the resistance between the contactor of potentiometer 65 andthe lower end of resistor 67 varies from (f-U f 9 to R. Thus, if 1equals 10, for example, the full scale movement of potentiometer 65produces a resistance variation from 0.9R to R. The spread of thepotentiometer over the upper tenth of its range is multiplied by ten andthe potentiometer must be moved ten times as fast as before to produce acorresponding change in resistance. In general, where the resistanceshave the values stated, full scale movement of the potentiometer armproduces a change in resistance of Accordingly, when the circuit ofFigure 4 is substituted for the potentiometer 47 of Figure 2, movementof crank 13x produces equal changes in the magnitude of v in the Figure2 units and the Figure 3 units so that the overall operation of thecircuit of Figure 1 is unchanged. The above relationship, of course,holds only when a negligible current is drawn from the contactor of thepotentiometer.

The function of the resistances 60, 62 and 63 in the described circuitis to provide a voltage at conductor 58 equal to When this voltage isprovided, it will be seen that the circuit functions in a manneranalogous of that of Figure 2. That is, a preselected fraction of avoltage existing between the contactor of potentiometer 55 and apreselected point 58 connected in circuit with the voltage supplyconductor 43 by potentiometer 60 and resistances 62 and 63 is comparedby means 40 with a reference voltage derived from potentiometer 52 toproduce a resultant voltage, the servomechanism including motor 49adjusting the voltage supply from potentiometer 41 to the resistancenetwork until the resultant voltage across means 40 becomes zero. Thevoltage may be derived from other circuits without departing from thespirit and scope of the invention. Furthermore, the values of resistors62, 63 may be varied and the circuit will still produce the desiredvoltage at conductor 58, although the setting of the potentiometer at Mwill, in general, be more complicated.

The circuit of Figure 3 is also eifectiveto increase the sensitivity ofa computer unit where the equilibrium constant of the component underconsideration becomes very large and v, the mol fraction of vapor in theentire mixture, approaches zero, corresponding physically to the caseWhere the component under consideration is extremely volatile but mostof the mixture is the liquid phase. In this case, potentiometer 57 isset so that C=fv. Since v is nearly equal to zero, its value ismultiplied by the factor 1 thus making it much easier to set thisparticular value upon the potentiometer. Potentiometer 55 is set so thatf D 2K Since K is very large is a small fraction which is multiplied bythe factor thus making this small fraction much easier to set upon thepotentiometer. Potentiometer 60 is set so that Substituting these valuesin Equation (13) gives In this case, the voltage at lead 43 isrepresentative of the percentage of the components in the vapor phase,rather than in the liquid phase. Accordingly, the voltage is applied toa terminal 26 of Figure l by a switch 43b. When this circuit is used,there is no point on the circuit corresponding to the value of x so thatthe value of x cannot be read from the ordinary circuits of thecomputer. In this case, the value of x is obtained by dividing the valueof y, by K It Will be noted that in this 'case, also, it is necessary'tospread the settings of the potentiometer 47 of the Figure 2 units, sothat all the potentiometers 47, 57 may be actuated jointly by crank 13x.This may be done mechanically or by substituting for each of thepotentiometers 4-7 a unit similar to that of Figure 4 except thatresistance 67 is positioned at the top rather than at the bottom of theshunted components 65, 66. Thus, the spreading occurs over the lowerpart of the potentiometer range, rather than over the upper part, as inFigure 4.

The function of the resistances 60, 62 and 63 in the last described unitis to provide a voltage at conductor 58 equal to V f l 2( K I When thisvoltage is provided, it will be seen that the circuit functions in amanner analogous of that of Figure 2. That is, a preselected fraction ofa voltage existing between the contactor of potentiometer 55 and apreselected point 58 connected in circuit with the voltage supplyconductor 43 by potentiometer 6t and resistances 62 and 63 is comparedat the amplifier 40 with a reference voltage derived from potentiometer52 to produce a resultant voltage, the servomechanism including motor 49adjusting the voltage supply to the resistance network until theresultant voltage across the input to means 40 becomes zero. The voltagemay be derived from other circuits without departing from the spirit andscope of the invention.

Thus, although the circuit of Figure 2 enables the computer to functionproperly for practically all values.

of K and V, the circuit of Figure 3 enables the computer to be used alsoin special cases Where the circuit of Figure 2 is somewhat insensitive.In some cases, where a special value of K is encountered for aparticular component, the sensitivity-increasing circuit of Figure 4 maybe substituted for the potentiometer 44 Without making any other changesin the apparatus, thus enabling the particular equilibrium constant ofthe component of interest to be set with greater accuracy. This alsoapplies to potentiometer 37 in case very small or very large values of Zshould be encountered. It will be evident, therefore, that the circuitof Figure 4, which increases the spread of a potentiometer over apreselected portion of its range by a factor f, has utilityindependently of the computer circuits described herein.

While the invention has been described in connection with presentpreferred embodiments thereof, it is to be understood that thisdescription is illustrative only and is not intended to limit theinvention.

I claim:

1. An electrical computer comprising, in combination, a voltage source;a plurality of units,- each of said units comprising a firstpotentiometer having the end terminals thereof connected across saidvoltage source, a second potentiometer having the end terminals thereofconnected across said voltage source, a third potentiometer having oneend terminal thereof connected to the con tactor of said secondpotentiometer and the second end terminal thereof connected to a pointof reference potential, a fourth potentiometer having one end terminalthereof connected to the contactor of said third potentiorneter andhaving the second end terminal thereof connected to the contactor ofsaid second potentiometer, means for comparing the potentials at thecontactors of said first and fourth potentiometers, means under controlof said comparing means to vary the contactor setting of said secondpotentiometer until there is zero potential difference between thecontactors of said first and fourth potcntiometers, an output terminal,and switching means to connect said output terminal selectively to thecontactors of said second and third otentiometers; means to vary thecontactor settings of the fourth potentiometers in each of said units inunison; means to sum the potentials from said output terminals of eachof said units; means connected to said voltage source to establish apotential of magnitude equal to the magnitude of said voltage sourcedivided by the number of said units; and means for comparing saidlast-mentioned potential with the summed potentials.

2. The combination in accordance with claim 1 further comprising amulti-position switch, the contacts of which are connected,respectively, to output terminals of said units, an adjustable means forproviding a voltage, a reversible motor having its drive shaft connectedto said adjustable means to adjust said voltage, means for applying theadjusted voltage and the voltage applied through said switch to theinput terminals of said motor in opposition, and means to indicate themagnitude of the adjusted voltage.

3. An electrical computer comprising, in combination, a voltage source;a plurality of units, each of said units comprising a firstpotentiometer having the. end terminals thereof connected across saidvoltage source, a second potentiometer having the end terminals thereofconnected across said voltage source, a third potentiometer having oneend terminal thereof connected to the contactor of said secondpotentiometer and the second end terminal thereof connected to a pointof reference potential, a fourth potentiometer having one end terminalthereof connected to the contactor of said second potentiometer andhaving the second end terminal thereof connected to said point ofreference potential, a first resistor having one end terminal thereofconnected to the contactor of said second potentiometer, a secondresistor having the first end terminal thereof connected to the secondend terminal of said first resistor and having the second end terminalthereof connected to the contactor of said fourth potentiometer, a fifthpotentiometer having one end terminal thereof connected to the contactorof said third potentiometer and having the second end terminal thereofconnected to the second terminal of said first resistor, means forcomparing the potentials at the contactors of said first and fifthpotentiometers, means under control of said comparing means to vary thecontactor setting of said second potentiometer until there is a zeropotential difference between the contactors of said first and fifthotentiometers, an output terminal connected to the contactor of saidsecond potentiometer; means to vary the contactor settings of the fifthpotentiometers in each of said units in unison; means to sum thepotentials from said output terminals in each of said units; meansconnected to said voltage source to establish a potential of magnitudeequal to the magnitude of said voltage source divided by the number ofsaid units; and means for comparing said last-mentioned potential withthe summed potentials.

4, The combination in accordance with claim 3 further comprising amult-i-posit-ion switch, the contacts of which are connected,respectively, to output terminals of said units, an adjustable means forproviding a voltage, a

reversible motor having its drive shaft connected to said adjustablemeans to adjust said voltage, means for applying the adjusted voltageand the voltage applied through said switch to the input terminals ofsaid motor in opposition, and means to indicate the magnitude of theadjusted voltage.

5. The combination in accordance with claim 1 further comprising, afirst resistor connected in series with said third potentiometer, and asecond resistor connected in shunt with said third potentiometer, theohmic value of said first resistor being and the ohmic value of saidsecond resistor being where R is the total resistance of said thirdpotentiometer and 7 is the factor by which the spread of said thirdpotentiometer is to be increased.

6. In a computer for determining the total fraction of vapor in avapor-liquid mixture at equilibrium, in combination, a plurality of ncircuits corresponding, respectively, to the several components of saidmixture, each of said circuits having a first branch that includes afirst variable impedance element representative of a function of thetotal fraction z of a particular component of the mixture, a secondbranch that includes a second variable impedance element representativeof a function of the equilibrium constant K of the particular componentof the mixture, and further includes a third variable impedance elementrepresentative of the fraction of vapor v in the mixture; means foradjusting simultaneously said last mentioned v-representative impedancesof all of said circuits; means for applying a reference potential E tosaid first and second branches in all of said circuits; and means tobalance the first branch of each circuit against the second branch ofeach circuit when said means for adjusting is operated and to produce anoutput signal When the said balance is achieved, said output signalhaving a potential equal to ZE l-t-(K-Dv means for adding the outputpotentials of said plurality of circuits; means for establishing asecond reference potential and means for comparing said second referencepotential with the sum of said output potentials.

7. In a computer for determining the total fraction of vapor in avapor-liquid mixture at equilibrium, in combination, a plurality of ncircuits corresponding, respectively, to the several components of saidmixture, each of said circuits having a first branch that includes afirst variable impedance element representative of a function of thetotal fraction z of a particular component of the mixture; a secondbranch that includes a second variable impedance element representativeof a function of the equilibrium constant K of the particular componentof the mixture; and further includes a thlrd variable 1mpedance elementrepresentative of the fraction of vapor v in the mixture; means foradjusting simultaneously said last mentioned v-representative impedancesof all of said circuits; means for applying a reference potent al E tosaid first and second branches in all of said circuits; and means tobalance the first branch of each circuit against the second branch ofeach clrcuit when said means for adjusting is operated and to produce anoutput signal when the said balance is achieved, said output signalhaving a potential equal to a plurality of resistors having firstterminals connected to the outputs of said circuits, respectively; aconductor connected to the second end terminals of said resistors; apotentiometer connected to said reference potential to establish asecond reference potential of magnitude and means for comparing saidsecond reference potential with the potential at said conductor.

8. An electrical computer comprising, in combination, a voltage source;a plurality of units, each of said units comprising a firstpotentiometer having the end terminals thereof connected across saidvoltage source, a second potentiometer having the end terminals thereofconnected across said voltage source, a third potentiometer having oneend terminal thereof connected to the contactor of said secondpotentiometer and the second end terminal thereof connected to a pointof reference potential, a fourth potentiometer, means for comparing thepotentials at the contactors of said first and fourth potentiometers,means under control of said comparing means to vary the contactorsetting of said second potentiometer until there is zero potentialdifference between the contactors of said first and fourthpotentiometers, and an output terminal connected to the contactor ofsaid second potentiometer; at least one of said units having a first endterminal of said fourth potentiometer connected to the contactor of saidsecond potentiometer; at least one of the other units having a fifthpotentiometer with one end terminal connected to the contactor of saidsecond potentiometer and having the second end terminal connected toreference potential; means to connect the contactor of said fifthpotentiometer to said first end terminal of said fourth potentiometer insaid at least one of the other units; means to vary the contactorsettings of all said fourth potentiometers in unison, including a meansfor causing adjustment of said fourth potentiometers in all of said atleast one units in proportion to the adjustment of all of said at leastone of the other units; means to sum the potentials from said outputterminals of each of said units; means connected to said source toestablish a potential of magnitude equal to the magnitude of saidvoltage source divided by the number of said units; and means forcomparing the current accompanying said last-mentioned potential withthe summed currents. I

9. The combination in accordance with claim 7 wherein at least one ofsaid first, second and third impedance elements comprises anotherpotentiometer, a first resistor connected in series with said anotherpotentiometer, and

a second resistor connected in shunt with said another potentiometer,the ohmic value of said first resistor being and the ohmic value of saidsecond resistor being where R is the total resistance of said anotherpotentiometer and f is the factor by which the spread of said anotherpotentiometer is to be increased.

10. In a computer wherein electrical outputs of a plurality of units aresummed, each unit providing an output voltage equal to the product of acommon voltage source and the mol fraction of a component in one phasein a vapor-liquid equilibrium mixture wherein the outputs of each ofsaid units are regulated by a single control representing the total molfraction of the mixture in one of the phases, a voltage balancingcircuit including a conductor; means for connecting each of said unitsto said conductor thereby to make said conductor common to the outputsof each of said units; means for applying a balance voltage to saidcommon conductor of magnitude equal to said common voltage divided bythe number of said units; current indicating means connected betweensaid balance voltage and said common conductor; a multi-position switch,the contacts of which are connected, respectively, to output terminalsof said units; an adjustable means for providing a voltage; a reversiblemotor having its drive shaft connected to said adjustable means toadjust the last-said voltage; means for applying the last-said voltageand the voltage applied to said switch to the input terminals of saidmotor in opposition; and means to indicate the magnitude of thelast-said voltage.

References Cited in the file of this patent lished by McGraw-Hill BookCo., New York, 1952, page 120.

